A thermal immersed boundary-lattice Boltzmann method for moving-boundary flows with Dirichlet and Neumann conditions

We construct a simple immersed boundary-lattice Boltzmann method for moving-boundary flows with heat transfer. On the basis of the immersed boundary-lattice Boltzmann method for calculating the fluid velocity and the pressure fields presented in the previous work by Suzuki and Inamuro (2011), the present method incorporates a lattice Boltzmann method for the temperature field combined with immersed boundary methods for satisfying thermal boundary conditions, i.e., the Dirichlet (iso-thermal) and Neumann (iso-heat-flux) conditions. We validate the present method through many benchmark problems including stationary and moving boundaries with iso-thermal and iso-heat-flux conditions, and we find that the present results have good agreement with other numerical results. Also, we investigate the internal heat effect through simulations of moving-boundary flows with heat transfer by using the present method. In addition, we apply the method to an interesting example of a moving-boundary flow with heat transfer, i.e., a two-dimensional thermal flow in a heated channel with moving cold particles, which is a simplified model of ice slurry flow.